Electroosmotic Velocity Research Articles

Electrothermal transport of nanofluids via peristaltic pumping in a finite micro-channel: Effects of Joule heating and Helmholtz-Smoluchowski velocity

The present article studies theoretically the electrokinetic pumping of nanofluids with heat and mass transfer in a micro-channel under peristaltic waves, a topic of some interest in medical nano-scale electro-osmotic devices. The microchannel walls are deformable and transmit periodic waves. The Chakraborty-Roy nanofluid electrokinetic formulation is adopted in which Joule heating effects are incorporated. Soret and Dufour cross-diffusion effects are also considered. Under low Reynolds number (negligible inertial effects), long wavelength and Debye linearization approximations, the governing partial differential equations for mass, momentum, energy and solute concentration conservation are derived with appropriate boundary conditions at the micro-channel walls. The merging model features a number of important thermo-physical, electrical and nanoscale parameter, namely thermal and solutal Grashof numbers, the Helmholtz-Smoluchowski velocity (maximum electro-osmotic velocity) and Joule heating to surface heat flux ratio. Closed-form solutions are derived for the solute concentration, temperature, axial velocity, averaged volumetric flow rate, pressure difference across one wavelength, and stream function distribution in the wave frame. Additionally expressions are presented for the surface shear stress function at the wall (skin friction coefficient), wall heat transfer rate (Nusselt number) and wall solute mass transfer rate (Sherwood number). The influence of selected parameters on these flow variables is studied with the aid of graphs. Bolus formation is also visualized and analyzed in detail.

Electro-osmotic flow of couple stress fluids in a micro-channel propagated by peristalsis

A mathematical model is developed for electro-osmotic peristaltic pumping of a non-Newtonian liquid in a deformable micro-channel. Stokes' couple stress fluid model is employed to represent realistic working liquids. The Poisson-Boltzmann equation for electric potential distribution is implemented owing to the presence of an electrical double layer (EDL) in the micro-channel. Using long wavelength, lubrication theory and Debye-Huckel approximations, the linearized transformed dimensionless boundary value problem is solved analytically. The influence of electro-osmotic parameter (inversely proportional to Debye length), maximum electro-osmotic velocity (a function of external applied electrical field) and couple stress parameter on axial velocity, volumetric flow rate, pressure gradient, local wall shear stress and stream function distributions is evaluated in detail with the aid of graphs. The Newtonian fluid case is retrieved as a special case with vanishing couple stress effects. With increasing the couple stress parameter there is a significant increase in the axial pressure gradient whereas the core axial velocity is reduced. An increase in the electro-osmotic parameter both induces flow acceleration in the core region (around the channel centreline) and it also enhances the axial pressure gradient substantially. The study is relevant in the simulation of novel smart bio-inspired space pumps, chromatography and medical micro-scale devices.

Effects of overlapping electric double layer on mass transport of a macro-solute across porous wall of a micro/nanochannel for power law fluid.

Effects of overlapping electric double layer and high wall potential on transport of a macrosolute for flow of a power law fluid through a microchannel with porous walls are studied in this work. The electric potential distribution is obtained by coupling the Poisson's equation without considering the Debye-Huckel approximation. The numerical solution shows that the center line potential can be 16% of wall potential at pH 8.5, at wall potential -73 mV and scaled Debye length 0.5. Transport phenomena involving mass transport of a neutral macrosolute is formulated by species advective equation. An analytical solution of Sherwood number is obtained for power law fluid. Effects of fluid rheology are studied in detail. Average Sherwood number is more for a pseudoplastic fluid compared to dilatant upto the ratio of Poiseuille to electroosmotic velocity of 5. Beyond that, the Sherwood number is independent of fluid rheology. Effects of fluid rheology and solute size on permeation flux and concentration of neutral solute are also quantified. More solute permeation occurs as the fluid changes from pseudoplastic to dilatant.

Faradaic Ion Concentration Polarization on a Paper Fluidic Platform.

We describe the design and characteristics of a paper-based analytical device for analyte concentration enrichment. The device, called a hybrid paper-based analytical device (hyPAD), uses faradaic electrochemistry to create an ion depletion zone (IDZ), and hence a local electric field, within a nitrocellulose flow channel. Charged analytes are concentrated near the IDZ when their electrophoretic and electroosmotic velocities balance. This process is called faradaic ion concentration polarization. The hyPAD is simple to construct and uses only low-cost materials. The hyPAD can be tuned for optimal performance by adjusting the applied voltage or changing the electrode design. Moreover, the throughput of hyPAD is 2 orders of magnitude higher than that of conventional, micron-scale microfluidic devices. The hyPAD is able to concentrate a range of analytes, including small molecules, DNA, proteins, and nanoparticles, in the range of 200-500-fold within 5 min.

Effects of Polymer Length and Salt Concentration on the Transport of ssDNA in Nanofluidic Channels

Electrokinetic phenomena in micro/nanofluidic channels have attracted considerable attention because precise control of molecular transport in liquids is required to optically and electrically capture the behavior of single molecules. However, the detailed mechanisms of polymer transport influenced by electroosmotic flows and electric fields in micro/nanofluidic channels have not yet been elucidated. In this study, a Langevin dynamics simulation was used to investigate the electrokinetic transport of single-stranded DNA (ssDNA) in a cylindrical nanochannel, employing a coarse-grained bead-spring model that quantitatively reproduced the radius of gyration, diffusion coefficient, and electrophoretic mobility of the polymer. Using this practical scale model, transport regimes of ssDNA with respect to the ζ-potential of the channel wall, the ion concentration, and the polymer length were successfully characterized. It was found that the relationship between the radius of gyration of ssDNA and the channel radius is critical to the formation of deformation regimes in a narrow channel. We conclude that a combination of electroosmotic flow velocity gradients and electric fields due to electrically polarized channel surfaces affects the alignment of molecular conformations, such that the ssDNA is stretched/compressed at negative/positive ζ-potentials in comparatively low-concentration solutions. Furthermore, this work suggests the possibility of controlling the center-of-mass position by tuning the salt concentration. These results should be applicable to the design of molecular manipulation techniques based on liquid flows in micro/nanofluidic devices.

ANALYTICAL STUDY OF ELECTRO-OSMOSIS MODULATED CAPILLARY PERISTALTIC HEMODYNAMICS

A mathematical model is developed to analyze electro-kinetic effects on unsteady peristaltic transport of blood in cylindrical vessels of finite length. The Newtonian viscous model is adopted. The analysis is restricted under Debye–Hückel linearization (i.e., wall zeta potential [Formula: see text] 25[Formula: see text]mV) is sufficiently small). The transformed, nondimensional conservation equations are derived via lubrication theory and long wavelength and the resulting linearized boundary value problem is solved exactly. The case of a thin electric double layer (i.e., where only slip electro-osmotic velocity considered) is retrieved as a particular case of the present model. The response in pumping characteristics (axial velocity, pressure gradient or difference, volumetric flow rate, local wall shear stress) to the influence of electro-osmotic effect (inverse Debye length) and Helmholtz–Smoluchowski velocity is elaborated in detail. Visualization of trapping phenomenon is also included and the bolus dynamics evolution with electro-kinetic effects examined. A comparative study of train wave propagation and single wave propagation is presented under the effects of thickness of EDL and external electric field. The study is relevant to electrophoresis in haemotology, electrohydrodynamic therapy and biomimetic electro-osmotic pumps.

Elastic deformations driven by non-uniform lubrication flows

The ability to create dynamic deformations of micron-sized structures is relevant to a wide variety of applications such as adaptable optics, soft robotics and reconfigurable microfluidic devices. In this work, we examine non-uniform lubrication flow as a mechanism to create complex deformation fields in an elastic plate. We consider a Kirchhoff–Love elasticity model for the plate and Hele-Shaw flow in a narrow gap between the plate and a parallel rigid surface. Based on linearization of the Reynolds equation, we obtain a governing equation which relates elastic deformations to gradients in non-homogeneous physical properties of the fluid (e.g. body forces, viscosity and slip velocity). We then focus on a specific case of non-uniform Helmholtz–Smoluchowski electro-osmotic slip velocity, and provide a method for determining the zeta-potential distribution necessary to generate arbitrary static and quasi-static deformations of the elastic plate. Extending the problem to time-dependent solutions, we analyse transient effects on asymptotically static solutions, and finally provide a closed form solution for a Green’s function for time periodic actuations.

Broadening of analyte streams due to a transverse pressure gradient in free-flow isoelectric focusing

Pressure-driven cross-flows can arise in free-flow isoelectric focusing systems (FFIEF) due to a non-uniform electroosmotic flow velocity along the channel width induced by the pH gradient in this direction. In addition, variations in the channel cross-section as well as unwanted differences in hydrostatic heads at the buffer/sample inlet ports can also lead to such pressure-gradients which besides altering the equilibrium position of the sample zones have a tendency to substantially broaden their widths deteriorating the separations. In this situation, a thorough assessment of stream broadening due to transverse pressure-gradients in FFIEF devices is necessary in order to establish accurate design rules for the assay. The present article describes a mathematical framework to estimate the noted zone dispersion in FFIEF separations based on the method-of-moments approach under laminar flow conditions. A closed-form expression has been derived for the spatial variance of the analyte streams at their equilibrium positions as a function of the various operating parameters governing the assay performance. This expression predicts the normalized stream variance under the chosen conditions to be determined by two dimensionless Péclet numbers evaluated based on the transverse pressure-driven and electrophoretic solute velocities in the separation chamber, respectively. Moreover, the analysis shows that while the stream width can be expected to increase with an increase in the value of the first Péclet number, the opposite trend will be followed with respect to the latter. The noted results have been validated using Monte Carlo simulations that also establish a time/length scale over which the predicted equilibrium stream width is attained in the system.

Electro-kinetically driven peristaltic transport of viscoelastic physiological fluids through a finite length capillary: Mathematical modeling

Analytical solutions are developed for the electro-kinetic flow of a viscoelastic biological liquid in a finite length cylindrical capillary geometry under peristaltic waves. The Jefferys’ non-Newtonian constitutive model is employed to characterize rheological properties of the fluid. The unsteady conservation equations for mass and momentum with electro-kinetic and Darcian porous medium drag force terms are reduced to a system of steady linearized conservation equations in an axisymmetric coordinate system. The long wavelength, creeping (low Reynolds number) and Debye–Hückel linearization approximations are utilized. The resulting boundary value problem is shown to be controlled by a number of parameters including the electro-osmotic parameter, Helmholtz–Smoluchowski velocity (maximum electro-osmotic velocity), and Jefferys’ first parameter (ratio of relaxation and retardation time), wave amplitude. The influence of these parameters and also time on axial velocity, pressure difference, maximum volumetric flow rate and streamline distributions (for elucidating trapping phenomena) is visualized graphically and interpreted in detail. Pressure difference magnitudes are enhanced consistently with both increasing electro-osmotic parameter and Helmholtz–Smoluchowski velocity, whereas they are only elevated with increasing Jefferys’ first parameter for positive volumetric flow rates. Maximum time averaged flow rate is enhanced with increasing electro-osmotic parameter, Helmholtz–Smoluchowski velocity and Jefferys’ first parameter. Axial flow is accelerated in the core (plug) region of the conduit with greater values of electro-osmotic parameter and Helmholtz–Smoluchowski velocity whereas it is significantly decelerated with increasing Jefferys’ first parameter. The simulations find applications in electro-osmotic (EO) transport processes in capillary physiology and also bio-inspired EO pump devices in chemical and aerospace engineering.

Electroosmosis over non-uniformly charged surfaces: modified Smoluchowski slip velocity for second-order fluids

In the present paper we focus on deriving the modified Smoluchowski slip velocity of second-order fluids, for electroosmotic flows over plane surfaces with arbitrary non-uniform surface potential in the presence of thin electric double layers (EDLs). We employ matched asymptotic expansion to stretch the electric double layer and subsequently apply regular asymptotic expansions taking the Deborah number ($De$) as the gauge function. Modified slip velocities correct up to $O(De^{2})$ are presented. Two sample cases are considered to demonstrate the effects of viscoelasticity on slip velocity: (i) an axially periodic patterned potential and (ii) a step-change-like variation in the surface potential. The central result of our analysis is that, unlike Newtonian fluids, the electroosmotic slip velocity for second-order fluids does not, in general, align with the direction of the applied external electric field. Proceeding further forward, we show that the slip velocity in a given direction may, in fact, depend on the applied electric field strength in a mutually orthogonal direction, considering three dimensionality of the flow structure. In addition, we demonstrate that the modified slip velocity is not proportional to the zeta potential, as in the cases of Newtonian fluids; rather it depends strongly on the gradients of the interfacial potential as well. Our results are likely to have potential implications so far as the design of charge modulated microfluidic devices transporting rheologically complex fluids is concerned, such as for mixing and bio-reactive system analysis in lab-on-a-chip-based micro-total-analysis systems handling bio-fluids.

Electrostatic interactions and electro-osmotic properties of semipermeable surfaces.

We consider two charged semipermeable membranes which bound bulk electrolyte solutions and are separated by a thin film of salt-free liquid. Small ions permeate into the gap, which leads to a steric charge separation in the system. To quantify the problem, we define an effective surface charge density of an imaginary impermeable surface, which mimics an actual semipermeable membrane and greatly simplifies the analysis. The effective charge depends on separation, generally differs from the real one, and could even be of the opposite sign. From the exact and asymptotic solutions of the nonlinear Poisson-Boltzmann equation, we obtain the distribution of the potential and of ions in the system. We then derive explicit formulae for the disjoining pressure in the gap and electro-osmotic velocity and show that both are controlled by the effective surface charge.

Electro-osmosis in inhomogeneously charged microporous media by pore-scale modeling

Surface charge at solid-electrolyte interface is generally coupled with the local electrolyte properties (ionic concentration, pH, etc.), and therefore not as assumed homogeneous on the solid surfaces in the previous studies. The inhomogeneous charge brings huge challenges in predictions of electro-osmotic transport and has never been well studied. In this work, we first propose a classification of electro-osmosis based on a dimensionless number which is the ratio of the Debye length to the characteristic pore size. In the limit of thin electrical double layer, we establish a pore-scale numerical model for inhomogeneously charged electro-osmosis including four ions: Na+,Cl-,H+ and OH-. Based on reconstructed porous media, we simulate the electro-osmosis with inhomogeneous charge using lattice Boltzmann method. The nonlinear response of electro-osmotic velocity to applied electrical field and the reverse flow have been observed and analyzed.

Enhancement of surface adsorption-desorption rates in microarrays invoking surface charge heterogeneity

This investigation is devoted to the influences of non-uniform wall characteristics on the surface adsorption-desorption rates in an electrokinetic microarray. Utilizing already explored electroosmotic and electrophoretic velocities, the species transport equations are solved by a finite-volume-based numerical approach. Uniform, sinusoidal, and pulse-like distributions of the zeta potential are considered in the analysis. The developed model is validated by comparing the results with those of two analytical solutions that are derived for limiting conditions. The results reveal that, in some cases, the surface charge heterogeneity can reduce the saturation time by more than 60%. The efficacy of the surface charge heterogeneity is limited to high Damkohler numbers and its effects are negligible for small values of this parameter. Whereas the impact of non-uniform surface characteristics is amplified by increasing the Peclet number, it is reduced by increasing either of the channel length to radius ratio or the electrophoretic mobility of the analytes.

Hofmeister effect for electrokinetic transport at ordered DNA layers

Development of DNA nanotechnology provides the basis to construct novel biomimetic DNA nanochannels. In this work, we report electrokinetic transport behavior of the fluid through the surfaces consisting of double-stranded DNA molecules based on all-atom molecular dynamics simulations. The results show that an electric double layer forms close to the DNA surface, and the fluid can be driven by an externally applied electric field. At large DNA–DNA separation, a velocity jump is observed when the electric field is exerted along the direction of the central axis of DNA. Increasing the DNA separation does not influence the flow velocity in the model parameters investigated. It was also found that the magnitude of electroosmotic flow velocity obeys the Hofmeister series.

Induced-charge electro-osmotic flow around cylinders with various orientations

Induced-charge electro-osmosis around multiple gold-coated stainless steel rods under various AC electric fields is investigated using the techniques of microparticle image velocimetry and numerical simulation. In this study, the results of interactions between induced electric double layers of two identical conductive cylinders on surrounding fluid are presented. The induced-charge electro-osmosis flow around multiple rods in touch and with one cylinder diameter gap reveals quadrupolar flow structures with four vortices. The induced-charge electro-osmotic flow structure and velocity magnitude also depend on the cylinder geometry and orientation. It is seen that four small vortices develop in the close region of cylinder surface for multiple rods with gap, while the other four large vortices are surrounding them. The distributions of vorticity patterns also strongly depend on cylinder orientation in the close region of cylinder surface.

Non-Negligible Diffusio-Osmosis Inside an Ion Concentration Polarization Layer

The first experimental and theoretical evidence was provided for the non-negligible role of a diffusio-osmosis in the ion concentration polarization (ICP) layer, which had been reported to be in a high Peclet number regime. Under the assumption that the hydrated shells of cations were stripped out with the amplified electric field inside the ICP layer, its concentration profile possessed a steep concentration gradient at the stripped location. Since the concentration gradient drove a strong diffusio-osmosis, the combination of electro-osmotic and diffusio-osmotic slip velocity had a form of an anomalous nonmonotonic function with both a single- and multiple-cationic solution. A direct measurement of electrolytic concentrations around the layer quantitatively validated our new investigations. This non-negligible diffusio-osmotic contribution in a micro- and nanofluidic platform or porous medium would be essential for clarifying the fundamental insight of nanoscale electrokinetics as well as guiding the engineering of ICP-based electrochemical systems.

AC Electroosmotic Pumping in Nanofluidic Funnels.

We report efficient pumping of fluids through nanofluidic funnels when a symmetric AC waveform is applied. The asymmetric geometry of the nanofluidic funnel induces not only ion current rectification but also electroosmotic flow rectification. In the base-to-tip direction, the funnel exhibits a lower ion conductance and a higher electroosmotic flow velocity, whereas, in the tip-to-base direction, the funnel has a higher ion conductance and a lower electroosmotic flow velocity. Consequently, symmetric AC waveforms easily pump fluid through the nanofunnels over a range of frequencies, e.g., 5 Hz to 5 kHz. In our experiments, the nanofunnels were milled into glass substrates with a focused ion beam (FIB) instrument, and the funnel design had a constant 5° taper with aspect ratios (funnel tip width to funnel depth) of 0.1 to 1.0. We tracked ion current rectification by current-voltage (I-V) response and electroosmotic flow rectification by transport of a zwitterionic fluorescent probe. Rectification of ion current and electroosmotic flow increased with increasing electric field applied to the nanofunnel. Our results support three-dimensional simulations of ion transport and electroosmotic transport through nanofunnels, which suggest the asymmetric electroosmotic transport stems from an induced pressure at the junction of the nanochannel and nanofunnel tip.

Transverse magnetic field driven modification in unsteady peristaltic transport with electrical double layer effects

The influence of transverse magnetic field on time-dependent peristaltic transport of electrically-conducting fluids through a microchannel under an applied external electric field with induced electric field effect is considered, based on lubrication theory approximations. The electrohydrodynamic (EHD) problem is also simplified under the Debye linearization. Closed-form solutions for the linearized dimensionless boundary value problem are derived. With increasing Hartmann number, the formation of bolus in the regime (associated with trapping) is inhibited up to a critical value of magnetic field. Flow rate, axial velocity and local wall shear stress are strongly decreased with greater Hartmann number whereas pressure difference is enhanced with higher Hartmann number at low time values but reduced with greater elapse in time. With greater electro-osmotic parameter (i.e. smaller Debye length), maximum time-averaged flow rate is enhanced, whereas the axial velocity is reduced. An increase in electrical field parameter (i.e. maximum electro-osmotic velocity) causes an increase in maximum time-averaged flow rate. The simulations find applications in electromagnetic peristaltic micro-pumps in medical engineering and also ⿿smart⿿ fluid pumping systems in nuclear and aerospace industries.

Time periodic electroosmotic flow of micropolar fluids through microparallel channel

The time periodic electroosmotic flow of an incompressible micropolar fluid between two infinitely extended microparallel plates is studied. The analytical solutions of the velocity and microrotation are derived under the Debye-H¨uckel approximation. The effects of the related dimensionless parameters, e.g., the micropolar parameter, the frequency, the electrokinetic width, and the wall zeta potential ratio of the upper plate to the lower plate, on the electroosmotic velocity and microrotation are investigated. The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1. The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid. However, the dependence of the microrotation on the related parameters mentioned above is complex. In order to describe these effects clearly, the dimensionless microrotation strength and the penetration depth of the microrotation are defined, which are used to explain the variation of the microrotation. In addition, the effects of various parameters on the dimensionless stress tensor at the walls are studied.

Viscoelectric effect on electroosmotic flow in a cylindrical microcapillary

Electroosmotic flow, under the Debye–Hückel approximation, has been widely analyzed in the specialized literature. This is a severe restriction in practice, where zeta potentials as high as 100–200 mV are encountered frequently. Under this condition, the variation of the viscosity with the electric field in the electric double layer (EDL), known as the viscoelectric effect, can lead to a considerable variation in comparison to the Helmholtz–Smoluchowsky equation for the electroosmotic velocity. The objective of this work is to analyze the electroosmotic flow in a cylindrical capillary at high zeta potentials in the thin EDL approximation, taking into account the viscoelectric effect. In order to obtain the potential distribution, the Poisson–Boltzmann equation was solved by using the matched asymptotic expansions method, and then, by applying the same technique, the flow field was determined from the momentum equation by considering that the viscosity of the electrolyte changes according to the relationship , where is the viscosity evaluated in the absence of an electric field, f is the viscoelectric constant and E is the intrinsic electric field in direction transversal to the EDL. For asserting the correctness of the asymptotic solution, this result was compared against a numerical solution, and a very good agreement between them was found. The results show that the viscoelectric effect has a noticeable influence by reducing the electroosmotic flow velocity in about 10% in comparison to the standard Helmholtz–Smoluchowski velocity.